Three mutually perpendicular chords in a sphere with radius R

Question

In a sphere, with radius R, there are three mutually perpendicular chords. They intersect at a point P (not the center). Point P divides the three chords into segments: a, b, c, d, e, f.

Is it true that: a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 6R^2

Answer 1

No, that's not true. More precisely, $$a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 2\,(3\,R^2-r^2),$$ where $r$ is the distance of $P$ from the center of the sphere.